A Markov chain representation of the multiple testing problem.

The problem of multiple hypothesis testing can be represented as a Markov process where a new alternative hypothesis is accepted in accordance with its relative evidence to the currently accepted one. This virtual and not formally observed process provides the most probable set of non null hypotheses given the data; it plays the same role as Markov Chain Monte Carlo in approximating a posterior distribution. To apply this representation and obtain the posterior probabilities over all alternative hypotheses, it is enough to have, for each test, barely defined Bayes Factors, e.g. Bayes Factors obtained up to an unknown constant. Such Bayes Factors may either arise from using default and improper priors or from calibrating p-values with respect to their corresponding Bayes Factor lower bound. Both sources of evidence are used to form a Markov transition kernel on the space of hypotheses. The approach leads to easy interpretable results and involves very simple formulas suitable to analyze large datasets as those arising from gene expression data (microarray or RNA-seq experiments).

Genetic correlations between measures of Mycobacterium bovis infection and economically important traits in Irish Holstein-Friesian dairy cows.

Mycobacterium bovis is the primary agent of tuberculosis (TB) in cattle. The failure of Ireland and some other countries to reach TB-free status indicates a need to investigate complementary control strategies. One such approach would be genetic selection for increased resistance to TB. Previous research has shown that considerable genetic variation exists for susceptibility to the measures of M. bovis infection, confirmed M. bovis infection, and M. bovis-purified protein derivative (PPD) responsiveness. The objective of this study was to estimate the genetic and phenotypic correlations between economically important traits and these measures of M. bovis infection. A total of 20,148 and 17,178 cows with confirmed M. bovis infection and M. bovis-PPD responsiveness records, respectively, were available for inclusion in the analysis. First- to third-parity milk, fat, and protein yields, somatic cell count, calving interval, and survival, as well as first-parity body condition score records, were available on cows that calved between 1985 and 2007. Bivariate linear-linear and threshold-linear sire mixed models were used to estimate (co)variance components. The genetic correlations between economically important traits and the measures of M. bovis infection estimated from the linear-linear and threshold-linear sire models were similar. The genetic correlations between susceptibility to confirmed M. bovis infection and economically important traits investigated in this study were all close to zero. Mycobacterium bovis-PPD responsiveness was positively genetically correlated with fat production (0.39) and body condition score (0.36), and negatively correlated with somatic cell score (-0.34) and survival (-0.62). Hence, selection for increased survival may indirectly reduce susceptibility to M. bovis infection, whereas selection for reduced somatic cell count and increased fat production and body condition score may increase susceptibility to M. bovis infection.